EBK MANUFACTURING PROCESSES FOR ENGINEE
EBK MANUFACTURING PROCESSES FOR ENGINEE
6th Edition
ISBN: 9780134425115
Author: Schmid
Publisher: YUZU
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Chapter 6, Problem 6.86P
To determine

The work done will be same for two specimens.

Expert Solution & Answer
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Answer to Problem 6.86P

The work done associated with specimen A and specimen B is not same.

Explanation of Solution

Given:

The height of the specimen A is ho1=50mm .

The cross section of the specimen A is a1=6.25×104m2 .

The height of the specimen B is ho2=25mm .

The cross section of the specimen B is a2=0.0025m2 .

The flash thickness is 5mm .

The largest strain in finishing forging is ε=0.25 .

Formula used:

The expression for the work done is given as,

  w=Fdho1   ............. (1)

Here, F is the force.

The expression for the force is given as,

  F=pavgA   ............. (2)

Here, pavg is the average pressure and A is the area.

The expression for the average pressure is given as,

  

  pavg=σf(1+2μr13h o1)   ............. (3)

Here, σf is the flow stress and r1 is the radius of specimen A and μ is the coefficient of friction.

The expression for volume is given as,

  v=πr12ho1   ............. (4)

Calculation:

Tre expression of specimen A radius from equation (4) can be calculated as,

  v=πr12ho1r1=v π h o1   ............. (5)

Now from equation (3) and (5),

  pavg=σf(1+ 2μ r 1 3 h o1 )pavg=σf(1+ 2μ( v π h o1 ) 3 h o1 )pavg=(σf( 1+( 2μ 3 )( v π )( 1 h 1 3 2 )))   ............. (6)

Substitute equation (6) in equation (2),

  F=(σf(1+( 2μ 3 )( v π )( 1 h o1 3 2 )))(vh o1)   ............. (7)

Substitute equation (7) in equation (1),

  w=( σ f ( 1+( 2μ 3 )( v π )( 1 h o1 3 2 ) ))( v h o1 )d h o1w=σfv h o h o 2 ( ( ( 1 h o1 )+( 2μ 3 )( v π )( 1 h o1 3 2 ) ))d h o1w=σfv( [ ln h o1 ] h o h o 2 32( 2μ π ) ( 1 h o1 3 2 ) h o h o 2 )   ............. (8)

Work done by the specimen A can be calculated as,

  w=σfv([ln h o2lnho]32( 2μ3)(vπ)(1 h o 3 2 2 1 h o 3 2 ))   ............. (9)

Substitute ho=50mm and v=6.25×104m2 in equation (9)

  w=σf(6.25× 10 4m2)( ( ( ln50mm× 1m 1000mm 2 )( ln50mm× 1m 1000mm ) ) μ( 6.25× 10 4 m 2 π )( 1 ( 50mm× 1m 1000mm 2 ) 3 2 1 ( 50mm× 1m 1000mm ) 3 2 ))w={ σ f( 6.25× 10 4 m 2 )( ( ln0.025m )( ln0.05m ))μ( 1.98× 10 4 m 2 )( 252.98 m 1 89.44 m 1 )}w=σf(6.25× 10 4m2)(0.6931m)μ(1.98× 10 4m2)(163.54m 1)w=σf(4.33× 10 4m3)μ(0.032m)

Work done by the specimen B can be calculated as,

Substitute ho=25mm and v=0.0025m2 in equation (9)

  w=σf(0.0025m2)( ( ( ln25mm× 1m 1000mm 2 )( ln25mm× 1m 1000mm ) ) μ( 0.0025 m 2 π )( 1 ( 25mm× 1m 1000mm 2 ) 3 2 1 ( 25mm× 1m 1000mm ) 3 2 ))w={ σ f( 0.0025 m 2 )( ln0.0125mln0.025m)μ( 7.95× 10 4 m 2 )( 715.54 m 1 252.98 m 1 )}w=σf(0.0025m2)(0.0693m)μ(0.3677m)w=σf(1.7325× 10 4m3)μ(0.3677m)

Conclusion:

Therefore, work done associated with specimen A and specimen B is not same.

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Chapter 6 Solutions

EBK MANUFACTURING PROCESSES FOR ENGINEE

Ch. 6 - Prob. 6.11QCh. 6 - Prob. 6.12QCh. 6 - Prob. 6.13QCh. 6 - Prob. 6.14QCh. 6 - Prob. 6.15QCh. 6 - Prob. 6.16QCh. 6 - Prob. 6.17QCh. 6 - Prob. 6.18QCh. 6 - Prob. 6.19QCh. 6 - Prob. 6.20QCh. 6 - Prob. 6.21QCh. 6 - Prob. 6.22QCh. 6 - Prob. 6.23QCh. 6 - Prob. 6.24QCh. 6 - Prob. 6.25QCh. 6 - Prob. 6.26QCh. 6 - Prob. 6.27QCh. 6 - Prob. 6.28QCh. 6 - Prob. 6.29QCh. 6 - Prob. 6.30QCh. 6 - Prob. 6.31QCh. 6 - Prob. 6.32QCh. 6 - Prob. 6.33QCh. 6 - Prob. 6.34QCh. 6 - Prob. 6.35QCh. 6 - Prob. 6.36QCh. 6 - Prob. 6.37QCh. 6 - Prob. 6.38QCh. 6 - Prob. 6.39QCh. 6 - Prob. 6.40QCh. 6 - Prob. 6.41QCh. 6 - Prob. 6.42QCh. 6 - Prob. 6.43QCh. 6 - Prob. 6.44QCh. 6 - Prob. 6.45QCh. 6 - Prob. 6.46QCh. 6 - Prob. 6.47QCh. 6 - Prob. 6.48QCh. 6 - Prob. 6.49QCh. 6 - Prob. 6.50QCh. 6 - Prob. 6.51QCh. 6 - Prob. 6.52QCh. 6 - Prob. 6.53QCh. 6 - Prob. 6.54QCh. 6 - Prob. 6.55QCh. 6 - Prob. 6.56QCh. 6 - Prob. 6.57QCh. 6 - Prob. 6.58QCh. 6 - Prob. 6.59QCh. 6 - Prob. 6.60QCh. 6 - Prob. 6.61QCh. 6 - Prob. 6.62QCh. 6 - Prob. 6.63QCh. 6 - Prob. 6.64QCh. 6 - Prob. 6.65QCh. 6 - Prob. 6.66QCh. 6 - Prob. 6.67QCh. 6 - Prob. 6.68QCh. 6 - Prob. 6.69QCh. 6 - Prob. 6.70QCh. 6 - Prob. 6.71QCh. 6 - Prob. 6.72QCh. 6 - Prob. 6.73PCh. 6 - Prob. 6.74PCh. 6 - Prob. 6.75PCh. 6 - Prob. 6.76PCh. 6 - Prob. 6.77PCh. 6 - Prob. 6.78PCh. 6 - Prob. 6.79PCh. 6 - Prob. 6.80PCh. 6 - Prob. 6.81PCh. 6 - Prob. 6.82PCh. 6 - Prob. 6.83PCh. 6 - Prob. 6.84PCh. 6 - Prob. 6.85PCh. 6 - Prob. 6.86PCh. 6 - Prob. 6.87PCh. 6 - Prob. 6.88PCh. 6 - Prob. 6.89PCh. 6 - Prob. 6.90PCh. 6 - Prob. 6.91PCh. 6 - Prob. 6.92PCh. 6 - Prob. 6.93PCh. 6 - Prob. 6.94PCh. 6 - Prob. 6.95PCh. 6 - Prob. 6.96PCh. 6 - Prob. 6.97PCh. 6 - Prob. 6.98PCh. 6 - Prob. 6.99PCh. 6 - Prob. 6.100PCh. 6 - Prob. 6.101PCh. 6 - Prob. 6.102PCh. 6 - Prob. 6.103PCh. 6 - Prob. 6.104PCh. 6 - Prob. 6.105PCh. 6 - Prob. 6.106PCh. 6 - Prob. 6.107PCh. 6 - Prob. 6.108PCh. 6 - Prob. 6.109PCh. 6 - Prob. 6.110PCh. 6 - Prob. 6.111PCh. 6 - Prob. 6.112PCh. 6 - Prob. 6.113PCh. 6 - Prob. 6.114PCh. 6 - Prob. 6.115PCh. 6 - Prob. 6.116PCh. 6 - Prob. 6.117PCh. 6 - Prob. 6.118PCh. 6 - Prob. 6.119PCh. 6 - Prob. 6.120PCh. 6 - Prob. 6.121PCh. 6 - Prob. 6.122PCh. 6 - Prob. 6.123PCh. 6 - Prob. 6.124PCh. 6 - Prob. 6.125PCh. 6 - Prob. 6.126PCh. 6 - Prob. 6.127PCh. 6 - Prob. 6.128PCh. 6 - Prob. 6.129PCh. 6 - Prob. 6.130PCh. 6 - Prob. 6.131PCh. 6 - Prob. 6.132PCh. 6 - Prob. 6.133PCh. 6 - Prob. 6.134PCh. 6 - Prob. 6.135PCh. 6 - Prob. 6.136PCh. 6 - Prob. 6.137PCh. 6 - Prob. 6.138PCh. 6 - Prob. 6.139PCh. 6 - Prob. 6.140PCh. 6 - Prob. 6.142DCh. 6 - Prob. 6.143DCh. 6 - Prob. 6.144DCh. 6 - Prob. 6.145DCh. 6 - Prob. 6.146DCh. 6 - Prob. 6.147DCh. 6 - Prob. 6.149D
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